Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
210 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C32×Dic3 | C2 | semidirect |
| 6. (C2×D3)⋊Dic3 | C3 | direct (N × H) |
| 10. C2×C32×D3 | C4 | semidirect |
| 18. C2×C3⋊Dic3 | C2×C3 | semidirect |
| 23. C2×C3×Dic3 | D3 | semidirect |
| 24. C2×C3×Dic3 | C2×C3 | semidirect |
| 49. C2×C3×D3 | Dic3 | semidirect |
| 50. C2×C3×D3 | C3×C4 | semidirect |
| 59. C33 | C22⋊C4 | semidirect |
| 71. C2×Dic3 | C3×D3 | semidirect |
| 116. C2×D3 | C3×Dic3 | semidirect |
| 129. C32 | (C2×D3)⋊C4 | semidirect |
| 130. C32 | #217 | semidirect |
| 131. C32 | C3×C22⋊C4 | semidirect |
| 170. C3 | (C2×D3)⋊Dic3 | direct (N × H) |
| 171. C3 | C3×(C2×D3)⋊C4 | semidirect |
| 172. C3 | C3×#217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D3 | 2 |
| C2×C3×C3⋊Dic3 | 2 |
| C2×C32×Dic3 | 2 |
| C3×#217 | 3 |
| C3×(C2×D3)⋊C4 | 3 |
| (C2×D3)⋊Dic3 | 3 |